Related papers: Robustness of statistical models

Let $M$ be an $n(\geq 4)$-dimensional compact submanifold in the simply connected space form $F^{n+p}(c)$ with constant curvature $c\geq 0$, where $H$ is the mean curvature of $M$. We verify that if the scalar curvature of $M$ satisfies…

In this note we introduce the notion of a smooth structure on a conical pseudomanifold $M$ in terms of $C^\infty$-rings of smooth functions on $M$. For a finitely generated smooth structure $C^\infty (M)$ we introduce the notion of the Nash…

For $\rho, v>0$, we say that an $n$-manifold $M$ satisfies local $(\rho,v)$-bound Ricci covering geometry, if Ricci curvature $\text{Ric}_M\ge -(n-1)$, and for all $x\in M$, $\text{vol}(B_\rho(\tilde x))\ge v>0$, where $\tilde x$ is an…

We investigate how the graph topology influences the robustness to noise in undirected linear consensus networks. We measure the structural robustness by using the smallest possible value of steady state population variance of states under…

Gaussian inference on smooth manifolds is central to robotics, but exact marginalization and conditioning are generally non-Gaussian and geometry-dependent. We study tangent-linearized Gaussian inference and derive explicit non-asymptotic…

We prove group existence and structure theorems in a general setting of tame topological theories. More precisely, we identify a linear/non-linear dividing line -- called topological 1-basedness -- among the class of t-minimal theories with…

Consider a compact manifold $M$ with smooth boundary $\partial M$. Suppose that $g$ and $\tilde{g}$ are two Riemannian metrics on $M$. We construct a family of metrics on $M$ which agrees with $g$ outside a neighborhood of $\partial M$ and…

Understanding which system structure can sustain stable dynamics is a fundamental step in the design and analysis of large scale dynamical systems. Towards this goal, we investigate here the structural stability of systems with a random…

We investigate weak and strong structures for generalized topological spaces, among others products, sums, subspaces, quotients, and the complete lattice of generalized topologies on a given set. Also we introduce $T_{3.5}$ generalized…

The main paradigm of smoothed analysis on graphs suggests that for any large graph $G$ in a certain class of graphs, perturbing slightly the edges of $G$ at random (usually adding few random edges to $G$) typically results in a graph having…

In several works, Mendel and Naor have introduced and developed theory surrounding a nonlinear expansion constant similar to the spectral gap for sequences of graphs, in which one considers embeddings of a graph $G$ into a metric space $X$…

We prove that for an induced CR structure on a compact, generic, regular 3-pseudoconcave CR submanifold ${\bold M}\subset{\bold G}$, of a complex manifold ${\bold G}$, satisfying condition $\dim H^1({\bold M}, T^{\prime}({\bold G})|_{\bold…

We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data…

We propose a microlocal-Riemannian framework for the three-dimensional incompressible Navier-Stokes equations on a smooth oriented Riemannian manifold (M,g). The dynamics is lifted to the unit cosphere bundle S*M via a normal-coordinate…

By using a Borel density theorem for algebraic quotients, we prove a theorem concerning isometric actions of a Lie group $G$ on a smooth or analytic manifold $M$ with a rigid $\mathrm{A}$-structure $\sigma$. It generalizes Gromov's…

We establish a rigidity theorem for Brendle and Hung's recent systolic inequality, which involves Gromov's notion of \(T^{\rtimes}\)-stabilized scalar curvature. Our primary technique is the construction of foliations by free boundary…

This paper introduces a new method for testing the statistical significance of estimated parameters in predictive regressions. The approach features a new family of test statistics that are robust to the degree of persistence of the…

Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models…

Let M be an open, connected manifold. A classical theorem of McDuff and Segal states that the sequence of configuration spaces of n unordered, distinct points in M is homologically stable with coefficients in Z: in each degree, the integral…

For a reductive group $G$, Harder-Narasimhan theory gives a structure theorem for principal $G$ bundles on a smooth projective curve $C$. A bundle is either semistable, or it admits a canonical parabolic reduction whose associated Levi…